Basin modeling/simulation, also known as petroleum system modeling/simulation, tracks the evolution of a sedimentary basin and its fluid content over geologic time scales of hundreds of millions of years by digitizing basin models and simulating interrelated processes associated with a basin. In recent years, it has become an important tool for the exploration geoscientists to predict types and presence of hydrocarbon (HC) fluids and to assess geologic risk before drilling exploratory wells to retrieve the HC fluids. A basin simulator often includes numerical modules to compute: 1) back-stripping and compaction; 2) pressure calculation; 3) heat flow analysis and kinetics; 4) petroleum generation, adsorption, and expulsion; 5) HC fluid phase behavior; and 6) HC migration and entrapments. Recently, invasion percolation (IP) has become a popular method to model secondary HC migration. Current commercial releases of basin modeling software have an IP method implemented only for serial computation, which is sufficiently fast for basin models up to a threshold of a few million cells. However, this threshold is an undesirable limitation for large-scale basin simulations where a fine-grid modeling of HC migration is desired.